Methods and systems for multi-fuel engine

A system, comprising:

• a first fuel system configured to supply a first fuel and coupled to a direct injector positioned to inject directly into a volume of a cylinder of an engine;
• a second fuel system configured to supply a second fuel and coupled to a port-fuel injector positioned to inject into an intake port of the cylinder, and the second fuel is different than the first fuel;
• a turbocharger having a turbine and a compressor;
• and
• a controller comprising computer-readable instructions stored on non-transitory memory thereof that when executed cause the controller to:
• compare a current substitution rate and a desired substitution rate of the first fuel and the second fuel;
• and
• adjust a speed of the turbocharger in response to the current substitution rate not matching the desired substitution rate.

A propulsion system for a vehicle, comprising:

• an engine comprising a cylinder;
• a first fuel system containing a first fuel and coupled to a direct injector positioned to inject directly into a volume of the cylinder;
• a second fuel system containing a second fuel and coupled to a port-fuel injector positioned to inject into an intake port of the cylinder, and the second fuel is different than the first;
• an electric turbocharger comprising an electric motor, a turbine and a compressor;
• and
• a controller comprising computer-readable instructions stored on non-transitory memory thereof that when executed cause the controller to adjust or maintain a substitution rate of the first fuel relative to the second fuel based at least in part on a highest available rotational speed of the compressor independent of rotational assistance from the electric motor.